# Who or what broke my kids?

June 1, 2014 6:47 PM Subscribe

Who or what broke my kids? "The basic premise of the activity is that students must sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability. I thought it would be an interactive way to gauge student understanding. Instead it turned into a ten minute nightmare where I was asked no less than 52 times if their answers were “right”. I took it well until I was asked for the 53rd time and then I lost it. We stopped class right there and proceeded to have a ten minute discussion on who broke them."

I can't wrap my head around how a teacher with any experience can seriously not know the answer to the question of who "broke" the kids.

posted by a box and a stick and a string and a bear at 7:03 PM on June 1, 2014 [9 favorites]

posted by a box and a stick and a string and a bear at 7:03 PM on June 1, 2014 [9 favorites]

So, maybe instead of trying to make the humanities more like STEM, we should make STEM more like the humanities?

(embittered humanist speaking)

posted by Saxon Kane at 7:09 PM on June 1, 2014 [33 favorites]

(embittered humanist speaking)

posted by Saxon Kane at 7:09 PM on June 1, 2014 [33 favorites]

Is standardized testing the right answer?

posted by Devils Rancher at 7:13 PM on June 1, 2014 [4 favorites]

posted by Devils Rancher at 7:13 PM on June 1, 2014 [4 favorites]

*In the end our meltdown and redo took more time than anticipated by me but it was time well worth it.*

Slight derail but it's super duper sad that the time crunch teachers feel is so bad that it makes it into an article like this.

*we must help them learn to stop looking for a right answer and start looking for a right reason.*

I turn from what seems like all of the science fiction I've consumed and weep at reality's interpretation of technological dependence/ignorance. So much of life in America is putting a problem into a black box and running with the answer it craps out the other end. Googling, GPS navigation, taxes, graphing calculators, spell check, even calculus—these technologies can be used at a distance from knowledge, and the information provided is presumed correct and whole.

What's lost, aside from the surety of verification, is the experience and strength gained from running your mind through the logistics of talking to a librarian or reading a map or tallying a balance sheet or using a dictionary or the crisp delight of a huge blank sheet of graph paper. In other words, turns out there's pudding in the proof.

posted by carsonb at 7:15 PM on June 1, 2014 [48 favorites]

High school algebra would have been so much easier and better if the oh-so-boring Mrs. Stark had explained

posted by double block and bleed at 7:17 PM on June 1, 2014 [17 favorites]

*why*we were expected to commit the quadratic formula to memory.posted by double block and bleed at 7:17 PM on June 1, 2014 [17 favorites]

Is she kidding? Everyone everywhere broke them. I can't remember any experience in school that wasn't about getting the right answer. I mostly got A's in math, and yet I'm pretty innumerate. After a certain point I didn't understand what I was doing, but I was smart enough to memorize formulas and get by. This stopped working around trig, so I just gave up and stoppped taking math classes because I didn't see any way I could catch up.

posted by Mavri at 7:18 PM on June 1, 2014 [26 favorites]

posted by Mavri at 7:18 PM on June 1, 2014 [26 favorites]

I question whether this is actually unusual or new. Even in the humanities, kids are rarely taught in a "no wrong answer" sort of way at that age, and for math, this is likely the first time they've run into the concept. I understand that we want children to be creative and to be able to think outside the box (or the test), but elementary school math doesn't lend itself to much beyond basic arithmetic, and it's hard to have much creative flexibility there.

Don't get me wrong, teaching by rote is stupid, and it's great that she's trying to push beyond that. (It's also great that statistics is apparently in the middle school curriculum now.) But the idea that your average 7th grader is "broken" because they want to know if they got it right is a bit of a stretch. Instead, it would be better to recognize that this is simply one more new concept to teach, and that it might take a while to sink in.

posted by tau_ceti at 7:19 PM on June 1, 2014 [10 favorites]

Don't get me wrong, teaching by rote is stupid, and it's great that she's trying to push beyond that. (It's also great that statistics is apparently in the middle school curriculum now.) But the idea that your average 7th grader is "broken" because they want to know if they got it right is a bit of a stretch. Instead, it would be better to recognize that this is simply one more new concept to teach, and that it might take a while to sink in.

posted by tau_ceti at 7:19 PM on June 1, 2014 [10 favorites]

The thing is, this person is teaching seventh graders, so 11 and 12 year-olds. Thinking back to my self at that age, I didn't give a damn about mathematics nor have any mathematical curiosity. I cared about getting the "right" answer because right answers lead to good grades which were directly tied to my allowance. The importance of intellectual curiosity to my future was something that I only understood in abstract,

Note: though I'm sure that this thread will cue all the people who

posted by Shouraku at 7:20 PM on June 1, 2014 [30 favorites]

*because I was 11 years old*.Note: though I'm sure that this thread will cue all the people who

*were*very intellectually curious at that age. No disrespect to those awesome people.posted by Shouraku at 7:20 PM on June 1, 2014 [30 favorites]

*Is standardized testing the right answer?*

Is it

*Ghostbusters 2*?

posted by Saxon Kane at 7:21 PM on June 1, 2014 [26 favorites]

Trying to convince students to worry about things other than "the right answer" when the system is designed to make their future success hugely dependent upon getting "the right answer" is absurd and idiotic. You wrote the rules of this game and you should expect students to try to win it.

posted by LastOfHisKind at 7:25 PM on June 1, 2014 [46 favorites]

posted by LastOfHisKind at 7:25 PM on June 1, 2014 [46 favorites]

I'm guessing it all happened because math of all things is about getting a right answer. And you really can get a right answer in math, with a provability only available in abstract domains.

Getting an estimate is a useful skill and can point you in the right direction but make no mistake, in all of lower mathematics if you don't know how to get and prove a correct answer you have not mastered the skill.

So she decided to break form and ask kids to give estimates. Good for her. Apparently she didn't explain her desires very well since after she threw a wobbler the kids did just fine.

The students on the other hand are in no way off base in assuming that they are attempting to find a right answer. Precision is a core element of mathematics and it is far better that they misunderstood in the direction of chasing it than not.

posted by Tell Me No Lies at 7:27 PM on June 1, 2014 [30 favorites]

Getting an estimate is a useful skill and can point you in the right direction but make no mistake, in all of lower mathematics if you don't know how to get and prove a correct answer you have not mastered the skill.

So she decided to break form and ask kids to give estimates. Good for her. Apparently she didn't explain her desires very well since after she threw a wobbler the kids did just fine.

The students on the other hand are in no way off base in assuming that they are attempting to find a right answer. Precision is a core element of mathematics and it is far better that they misunderstood in the direction of chasing it than not.

posted by Tell Me No Lies at 7:27 PM on June 1, 2014 [30 favorites]

*Trying to convince students to worry about things other than "the right answer" when the system is designed to make their future success hugely dependent upon getting "the right answer" is absurd and idiotic. You wrote the rules of this game and you should expect students to try to win it.*--LastOfHisKind

I don't know about that. I work in engineering design and if our group just went for the first design that seemed to solve the industry's problems, our competitors would be eating our lunch. By trying to solve future problems, you can keep ahead. But what are the future problems? There's no right answer. There are only intelligent guesses, creativity, and luck.

posted by eye of newt at 7:35 PM on June 1, 2014 [11 favorites]

*The importance of intellectual curiosity to my future was something that I only understood in abstract, because I was 11 years old.*

I've been doing scientific outreach with kids for almost 20 years now, working with school-aged students from urban, rural and isolated geographic areas. 11-12 year old students are, almost without exception, an absolute pleasure to teach. Particularly when you engage them in questions-driven learning activities.

Students at this age just seem to be at the pinnacle of their childhood learning: they're curious, intelligent, responsible kids. Then they hit adolescence and they have to start re-learning how to live within an entirely new set of rules and experiences.

posted by Alice Russel-Wallace at 7:36 PM on June 1, 2014 [22 favorites]

*When did we brainwash kids into thinking that math was about getting an answer? My students truly believe for some reason that math is about combining whatever numbers you can in whatever method that seems about right to get one “answer” and then call it a day.*

Assuming you are sampling an "average" group of kids to get an "average" test cohort (quite an assumption, since sociaeconomic stratification means there will be kids who, because of their background, are "good" at school, and attend school with other kids who are good at school, versus other classes in, say, poorer neighbourhoods with kids who are bad at school go to school with kids who are bad at school), there are always going to be kids who don't "get" math.

It could be because of their cognitive ability. At age 12 or 13, there are going to be kids still at the "concrete operational" stage who operate according to rules, and in generally a very linear fashion.

From their point of view (at that particular point and time in their cognitive development) all that matters is a right answer, rather than the process.

From my point of view, asking the kids to "sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability" (source pdf) seems kind of tedious.

So kudos to the teacher for forging on.

This seemed really interesting:

*Why Constructing a Viable Argument and Making Sense of the Reasoning of Others is Crucial*

I think it's great, but you know I don't remember doing that studying algebra with Mr. Ridley way back in 1986. Algebra was pretty fun an interesting, since it operated according to a strict set of rules, the order of operations.

I think one of the challenges a teacher has teaching abstract subjects like math to adolescents is that adolescents aren't particularly interested in school.

They are going through puberty and are learning more about how to interact socially. In some ways it may be a good idea to send them all to sports camp or something at age 13, and then bring them back to school at age 15 or 16.

posted by KokuRyu at 7:39 PM on June 1, 2014 [5 favorites]

*Students at this age just seem to be at the pinnacle of their childhood learning: they're curious, intelligent, responsible kids. Then they hit adolescence and they have to start re-learning how to live within an entirely new set of rules and experiences.*

I say yet again:

No disrespect to those awesome people.

posted by Shouraku at 7:39 PM on June 1, 2014

Students treat school like adults treat jobs; 90% of the time you are on autopilot,

You have to be that way, because your day is carved into little 50-minute chunks; it doesn't make sense for you to be wholly absorbed in Math, because soon you'll be scurrying to History and have to start over.

And you probably stayed up late the night before working on fanfic or learning guitar or whatever it is that you

If the teacher insists (as she does here) or class happens to be about something you care about, then yes, you are quite capable of getting absorbed and engaged. Just as can happen at work when you get a problem out of the norm, you can shake off the autopilot and turn your brain back on.

But school is not really designed for you to be that way. The kids aren't broken; they've adapted to the system they are in. To get what she wants would require a less-structured Montessori-type approach.

posted by emjaybee at 7:42 PM on June 1, 2014 [42 favorites]

*and that works fine*. Go to class on time, sit down, listen, do what the teacher wants to get Right Answer (or just hope they don't call on you because you didn't read the assignment), go to next class, etc. until you go home.You have to be that way, because your day is carved into little 50-minute chunks; it doesn't make sense for you to be wholly absorbed in Math, because soon you'll be scurrying to History and have to start over.

And you probably stayed up late the night before working on fanfic or learning guitar or whatever it is that you

*truly*care about.If the teacher insists (as she does here) or class happens to be about something you care about, then yes, you are quite capable of getting absorbed and engaged. Just as can happen at work when you get a problem out of the norm, you can shake off the autopilot and turn your brain back on.

But school is not really designed for you to be that way. The kids aren't broken; they've adapted to the system they are in. To get what she wants would require a less-structured Montessori-type approach.

posted by emjaybee at 7:42 PM on June 1, 2014 [42 favorites]

For real tho I still am not sure about the weather. If it said on the news last night there is a 60% chance of rain today, but it doesn't rain, doesn't that mean there was actually a 0% chance of rain?

posted by Potomac Avenue at 7:44 PM on June 1, 2014 [2 favorites]

posted by Potomac Avenue at 7:44 PM on June 1, 2014 [2 favorites]

*When did we brainwash kids into thinking that math was about getting an answer?*

I started Kindergarten in 1978. So, sometime before 1978.

posted by Slap*Happy at 7:50 PM on June 1, 2014 [11 favorites]

Potomac Avenue: This is a truly deep question and you just bought a book in which it's discussed!

posted by escabeche at 7:50 PM on June 1, 2014 [3 favorites]

posted by escabeche at 7:50 PM on June 1, 2014 [3 favorites]

The kids are all, "Right?"

posted by 2bucksplus at 7:52 PM on June 1, 2014 [29 favorites]

posted by 2bucksplus at 7:52 PM on June 1, 2014 [29 favorites]

*If it said on the news last night there is a 60% chance of rain today, but it doesn't rain, doesn't that mean there was actually a 0% chance of rain?*

It means that it rained on 60% of the days that were like today. meteorologically like today, not like today in that today is Sunday or your birthday or whatever.

posted by thelonius at 7:53 PM on June 1, 2014 [4 favorites]

Every once in a while I get this very overwhelming sense of relief that I'll probably never have to take another math test again.

posted by hellojed at 7:53 PM on June 1, 2014 [6 favorites]

posted by hellojed at 7:53 PM on June 1, 2014 [6 favorites]

This seems to be a rather vague plea for more critical thought than anything particularly to do with math. At the age I think seventh grade kids are (I can never remember which grade is what age; I'm British), math pretty much

That 50% conclusion is a classic fallacy of probability estimation that should have been nailed, there and then. My old maths teacher would have been all over that like a rash. Perhaps the fact that (apparently) teachers no longer do that sort of thing explains why I frequently see this exact fallacy from adults who really ought to know better (e.g. certain probabilistic arguments for the existence of God by the likes of Stephen D. Unwin, that include the assumption that since God either exists or not the odds of his existence can be assumed to be 50%).

posted by Decani at 7:55 PM on June 1, 2014 [9 favorites]

*is*about "getting the right answer", and I suspect it was ever thus. But a good teacher - of math or anything else - will always encourage kids to think about and discuss*why*it is the right answer. For example:*One student had seen the weather and knew there was a 90% chance of rain the other had not seen the weather and though the probability was 50% since it would either rain or not.*That 50% conclusion is a classic fallacy of probability estimation that should have been nailed, there and then. My old maths teacher would have been all over that like a rash. Perhaps the fact that (apparently) teachers no longer do that sort of thing explains why I frequently see this exact fallacy from adults who really ought to know better (e.g. certain probabilistic arguments for the existence of God by the likes of Stephen D. Unwin, that include the assumption that since God either exists or not the odds of his existence can be assumed to be 50%).

posted by Decani at 7:55 PM on June 1, 2014 [9 favorites]

Man [used advisedly] am I ever blushing-- until I glanced at the photo-icon in the comments section, I was misreading the teacher's name as Brooks Powers, and assuming she was male.

posted by jamjam at 7:57 PM on June 1, 2014

posted by jamjam at 7:57 PM on June 1, 2014

Potomac Avenue, my understanding of the weather forecast is that a 60% chance of rain means that in your geographical area, rain will fall on about 60% of that area. Therefore there is a 60% chance of it falling where you are.

posted by ThatCanadianGirl at 7:58 PM on June 1, 2014

posted by ThatCanadianGirl at 7:58 PM on June 1, 2014

*a 60% chance of rain means that in your geographical area, rain will fall on about 60% of that area*

No, but this is a common misconception.

posted by thelonius at 8:04 PM on June 1, 2014 [13 favorites]

*Potomac Avenue, my understanding of the weather forecast is that a 60% chance of rain means that in your geographical area, rain will fall on about 60% of that area. Therefore there is a 60% chance of it falling where you are.*

Almost, but not quite. It's area times probability. So one interpretation is that there is 100% chance it will fall on 60% of the area. 100% of 60% = 60%

Another is that there's a 60% chance it'll fall on 100% of the area (and a 40% chance it won't rain at all). And everything in between.

I mean, if you flip a coin, there's a 50% chance it's going to land on heads. If it lands on tails, does that actually mean there was a 0% chance it was going to land on heads?

posted by RustyBrooks at 8:05 PM on June 1, 2014 [3 favorites]

Maybe my school was weird -- although I went to public school -- but I do remember a unit in which we learned how to estimate and were taught that estimation is important because otherwise how can we be sure that the output of what we punch into a calculator is a reasonable answer?

I think it's great that these kids are being exposed to the concept of probability, and also being taught to rely on their own judgment, which is a crucial skill in life, arguably equal or greater in importance to understanding math (which makes it even awesomer that they're being taught in tandem with each other).

posted by spacewaitress at 8:05 PM on June 1, 2014 [4 favorites]

I think it's great that these kids are being exposed to the concept of probability, and also being taught to rely on their own judgment, which is a crucial skill in life, arguably equal or greater in importance to understanding math (which makes it even awesomer that they're being taught in tandem with each other).

posted by spacewaitress at 8:05 PM on June 1, 2014 [4 favorites]

But it's today and it didn't rain!

hooray! :)

posted by Potomac Avenue at 8:05 PM on June 1, 2014 [1 favorite]

*Potomac Avenue: This is a truly deep question and you just bought a book in which it's discussed!*hooray! :)

posted by Potomac Avenue at 8:05 PM on June 1, 2014 [1 favorite]

As others have said, this seems nothing remotely new.

When I was at school some 50 years ago, mathematics was entirely about "trick and tick" - every question had a "right" answer. It pervaded other subjects; you did physics experiments, and an experiment that got the 'right' value (e.g. for the speed of sound, or the density of a metal) got the marks. I don't recall being introduced to the idea of estimation, or of open-ended experiments where the 'right' answer was unknown, or altered by some inherent measurement error, until university.

posted by raygirvan at 8:06 PM on June 1, 2014

When I was at school some 50 years ago, mathematics was entirely about "trick and tick" - every question had a "right" answer. It pervaded other subjects; you did physics experiments, and an experiment that got the 'right' value (e.g. for the speed of sound, or the density of a metal) got the marks. I don't recall being introduced to the idea of estimation, or of open-ended experiments where the 'right' answer was unknown, or altered by some inherent measurement error, until university.

posted by raygirvan at 8:06 PM on June 1, 2014

maybe because, extrapolating from the skills of your average college freshman, your class of 11 and 12 year old can barely handle arithmetic operations with fractions. yet, because some committee decided probability is important you are talking about things which only make sense if fractions make sense... I.e. numbers between 0 and 1.

the answer is you, you broke your own kids.

posted by ennui.bz at 8:10 PM on June 1, 2014 [1 favorite]

the answer is you, you broke your own kids.

posted by ennui.bz at 8:10 PM on June 1, 2014 [1 favorite]

*I mean, if you flip a coin, there's a 50% chance it's going to land on heads. If it lands on tails, does that actually mean there was a 0% chance it was going to land on heads?*

Well. We are in the universe where you did, in fact, get tails on that throw. So, I guess there is probably some philosophical position that says there was indeed a 0% chance that you could have thrown heads then. But that would go way off from the mathematical study of probability as expected result, repeated trials, and all that, into metaphysics. I don't even know if metaphysics is in the Common Core standards. People have told me, with burning light in their eyes, that everything that is possible must eventually occur. How do they know that?

posted by thelonius at 8:17 PM on June 1, 2014 [6 favorites]

There was a 60% percent chance that it

posted by I-Write-Essays at 8:21 PM on June 1, 2014 [1 favorite]

*would*rain, and there is a 0% chance that it*did*rain (Unless you're not entirely sure whether it rained or not).posted by I-Write-Essays at 8:21 PM on June 1, 2014 [1 favorite]

*If You Can Type the Problem into Wolfram Alpha and Get an Answer You Aren’t Doing Math*

If you can check the correctness of your calculations in Wolfram Alpha, you're doing math.

Sorry teacher, YOU broke the kids. You taught the lesson badly.

BTW, remarks like this absolutely infuriate me:

*Assuming you are sampling an "average" group of kids to get an "average" test cohort (quite an assumption, since sociaeconomic stratification means there will be kids who, because of their background, are "good" at school, and attend school with other kids who are good at school, versus other classes in, say, poorer neighbourhoods with kids who are bad at school go to school with kids who are bad at school), there are always going to be kids who don't "get" math.*

Poor kids are bad at school, rich kids are good at school, amirite?

posted by charlie don't surf at 8:23 PM on June 1, 2014 [7 favorites]

*My students truly believe for some reason that math is about combining whatever numbers you can in whatever method that seems about right to get one “answer” and then call it a day.*

Hopefully it's different now, but math was absolutely taught that way in the schools I went to. Full credit for right answers with work shown, partial credit sometimes for wrong answers with work shown or right answers with no work, and no credit for just plain wrong. And that partial credit for having work shown was sometimes a red herring, because if you showed all the work and it was all the right steps, shouldn't you have the right answer? (Obviously not, but that was not always reflected in the grading.)

posted by Dip Flash at 8:27 PM on June 1, 2014 [2 favorites]

I think I recognize her blog and she always seems like a really good, really caring teacher. I wonder what her annual salary is?

posted by benito.strauss at 8:31 PM on June 1, 2014 [2 favorites]

posted by benito.strauss at 8:31 PM on June 1, 2014 [2 favorites]

I understand this educator's grief. I've been there. Sometimes, I've noticed something was up before the classroom's pendulum swung too far towards the "let's find the 'right' answer and let's finish this activity", and sometimes not. Sometimes I've felt like I actively emphasized the idea the math is not about The Right Answer

My story, then, is no different, than any teacher. Win some, lose some.

For the "lose some" lessons, the ones that send you home asking (slash blogging) about "who broke our kids???" I've tried hard to ask myself, personally, the 'opposite' question posed by the article. Less "who broke our kids???" but "from whence enlightenment???" (okay, YMMV on how to formulate an 'opposite' question)

And let's be honest: the answers to such an 'opposite' question will be as varied as those individuals speaking from 'the know'. I can't speak to all of them directly. But I know that I can speak quite candidly about my experiences in seeing mathematics as more than The Right Answer

My style: easily seen to be incompatible with standardized test prep. But, as my the old saw goes, "I teach students, not math." Far as I'm concerned, The Right Answer

posted by Theophrastus Johnson at 8:43 PM on June 1, 2014 [4 favorites]

^{TM}, sometimes I've felt like my teaching reactively makes that point, after a class gone frustratingly wrong.My story, then, is no different, than any teacher. Win some, lose some.

For the "lose some" lessons, the ones that send you home asking (slash blogging) about "who broke our kids???" I've tried hard to ask myself, personally, the 'opposite' question posed by the article. Less "who broke our kids???" but "from whence enlightenment???" (okay, YMMV on how to formulate an 'opposite' question)

And let's be honest: the answers to such an 'opposite' question will be as varied as those individuals speaking from 'the know'. I can't speak to all of them directly. But I know that I can speak quite candidly about my experiences in seeing mathematics as more than The Right Answer

^{TM}. In the high school (and early/developmental college) mathematical universe, where the aura of The Right Answer^{TM}can hold unimaginable sway, this candor -- that my way to solve it isn't The Way To Solve It -- can engage students otherwise predisposed to view math as a nuisance, a chore, a search for The Answer-and-onto-the-next-course.My style: easily seen to be incompatible with standardized test prep. But, as my the old saw goes, "I teach students, not math." Far as I'm concerned, The Right Answer

^{TM}and $0.75 will get you a cup of coffee, you know?posted by Theophrastus Johnson at 8:43 PM on June 1, 2014 [4 favorites]

This thread is really about pre-college teaching, so my comment may be mis-targeted, but anyway...

Maybe so.

I teach theoretical computer science at a top-tier university, and I found to my surprise that though the students usually understood the math really well, they were often at a complete loss when it came to, "what does it mean?", "why is it important?", "where does it apply?", "what are good examples or counterexamples?", "what related issues or variations would be interesting?" i.e. to engage the material personally. I similarly found that students typically could solve well-posed technical problems, but often had no idea how to approach a "problem" or "thing of interest" before it had been translated into equations. So I asked myself what made the big difference in my own education -- and came up with the answer that it was my classes in the humanities: critical reading of and discussion of Aristotle's metaphysics, texts in history, sociology, philosophy, etc. where I was constantly provoked to distinguish meaning from bullshit and to form and explore my own opinions.

So I decided to try teaching information theory and complexity theory as a "humanities class". Students read the material ahead of time, we meet and sit around a table, students discuss what the theorems mean, explore counter examples, mention ideas they had on the side, alternative proofs, invent their own "homework problems", debate what the essential idea is…

I had fun. So did the students.

This probably wouldn't work for all students everywhere, but perhaps if teaching at the high school level and below wasn't so broken, maybe teaching STEM a bit more like the humanities could be a good thing.

posted by brambleboy at 9:07 PM on June 1, 2014 [23 favorites]

*So, maybe instead of trying to make the humanities more like STEM, we should make STEM more like the humanities?*Maybe so.

I teach theoretical computer science at a top-tier university, and I found to my surprise that though the students usually understood the math really well, they were often at a complete loss when it came to, "what does it mean?", "why is it important?", "where does it apply?", "what are good examples or counterexamples?", "what related issues or variations would be interesting?" i.e. to engage the material personally. I similarly found that students typically could solve well-posed technical problems, but often had no idea how to approach a "problem" or "thing of interest" before it had been translated into equations. So I asked myself what made the big difference in my own education -- and came up with the answer that it was my classes in the humanities: critical reading of and discussion of Aristotle's metaphysics, texts in history, sociology, philosophy, etc. where I was constantly provoked to distinguish meaning from bullshit and to form and explore my own opinions.

So I decided to try teaching information theory and complexity theory as a "humanities class". Students read the material ahead of time, we meet and sit around a table, students discuss what the theorems mean, explore counter examples, mention ideas they had on the side, alternative proofs, invent their own "homework problems", debate what the essential idea is…

I had fun. So did the students.

This probably wouldn't work for all students everywhere, but perhaps if teaching at the high school level and below wasn't so broken, maybe teaching STEM a bit more like the humanities could be a good thing.

posted by brambleboy at 9:07 PM on June 1, 2014 [23 favorites]

*I'm guessing it all happened because math of all things is about getting a right answer. And you really can get a right answer in math, with a provability only available in abstract domains.*

No.

Math, as an academic discipline, is the study of sets, patterns, numbers, shapes - things that can be defined in a particular abstract and precise way, and reasoned about with deductive logic. But the definitions are sometimes kind of arbitrary, and what mathematicians consider the product of mathematical research is an argument (i.e. a mathematical proof). It so happens that a lot of the things that we have arguments for being true (given certain basic assumptions/definitions or axioms) are very useful in a lot of other contexts.

As for math as a practical tool outside of academia and pure mathematics: the story used to frame the presentation of mathematical logic in the book Logicomix describes a talk that Bertrand Russell gave on what is math good for, and Russell's answer was essentially that math teaches you how to think. That is, the skills of quantitative, analytical, deductive, and logical reasoning are the the most important things one can get from learning math; not rote memorization of certain math facts or computational algorithms (though those are often useful as well). These reasoning skills are all sorts of useful in many contexts outside of formal mathematical systems - contexts, for example, where you don't have as much certainty or precision in definitions and axioms, and thus where there truly is no "right answer", but where you can use the reasoning skills that you learned from math to generate or make decisions about a best answer given context.

Students can easily (and to their general happiness) be taught math as reasoning. Bill Ayers has a nice example of this for very young students, with a kindergarten class figuring out how to best build a ramp for their class' pet turtle, in To Teach: The Journey in Comics. Probably a large part of why I ended up as a mathematician (or at least had that option open to me) was early educational and school experiences where math was taught as puzzles and as reasoning, and where I was taught the "why" behind the computational algorithms that I had to learn and apply. For additional examples of how one can teach math as reasoning (with computation also, but explaining the why behind everything), the book Measurement by Paul Lockhart is very approachable and readable, according to my non-mathematical friends who have humored me and read it.

posted by eviemath at 9:10 PM on June 1, 2014 [17 favorites]

I am in a terrible mood already, but I hate this essay? First of all, if the exercise is about getting the students to use critical thinking skills and there are many possible right answers, would it kill you to tell them that at the outset? Because I'm pretty sure that when you give the kids quizzes and tests, you don't care about their novel explanation for the probability of rain tomorrow, you care about whether they understand probability or not. It's not

I also hate the teacher trope that it's broken to care about being right

This seems like...not a bad way to approach math to me? Isn't a huge part of math literacy being able to interpret which values in a problem are relevant and how to combine those values to solve some sort of...you know...

posted by Snarl Furillo at 9:10 PM on June 1, 2014 [22 favorites]

*crazy and broken*of them to assume that this is one of those instances where being right matters if you don't tell them otherwise.I also hate the teacher trope that it's broken to care about being right

*at all*. Some of us learn by making sure each step of the process is right before moving on to the next. If I'm supposed to build this number line to understand the difference between "likely" and "certain" and the relationship between "85%" and "likely" and "1" and "certain," then I want to know if putting likely before certain on the line is correct before the exercise is over and it turns out, whoops, I didn't understand that progression at all. It's not broken to want that, or to want to check your work with*the one person in the room who knows what the fuck is going on*before you move on to the next part. Like, what is the point of having a qualified instructor in the room if the idea is to make up your own justification for what a shaded circle means and every justification is equally good? Right now there are a bunch of seventh-graders who developed a probability system using shaded and unshaded circles in which*there is no symbol for zero*. They didn't get to the deeper understanding that you should be able to represent every outcome in the same symbolic language, because their teacher thought they were broken for caring about the right answer. Great.*My students truly believe for some reason that math is about combining whatever numbers you can in whatever method that seems about right to get one “answer” and then call it a day. They rarely think about what they are doing as long as at the end of the day their answer is “correct”.*This seems like...not a bad way to approach math to me? Isn't a huge part of math literacy being able to interpret which values in a problem are relevant and how to combine those values to solve some sort of...you know...

*problem*? Being able to gather or interpret a set of values, pick out the two or three that will help you discern some previously unknown information, and then choosing the correct method out of the many you know to yield a useful answer that you didn't have before strikes me as actually a pretty sophisticated set of mathematical skills and not evidence that a bunch of 12-year-olds are mindless automatons.posted by Snarl Furillo at 9:10 PM on June 1, 2014 [22 favorites]

*My old maths teacher would have been all over that like a rash.*

I had a freshman university professor who charmingly addressed the 50% fallacy with: "Sure, that's one way to look at probability. Anything either happens, or it doesn't. So you get 50%. The problem is that you get 50% for everything. That's great when you're thinking about winning the lottery, and not so great when you're worried about whether the nuclear reactor will explode today. We need a different way, that distinguishes likely events from unlikely ones, so instead we measure probability like this....", and proceeded to teach the rest of the introductory course.

But that was in a post-secondary school with a reputation for putting emphasis on the fundamentals. It needs to happen more at the high school and elementary school level, but Right Answers are so much easier to measure in standardized tests.

posted by ceribus peribus at 9:12 PM on June 1, 2014 [9 favorites]

And that's where the money is.

posted by carping demon at 9:25 PM on June 1, 2014

posted by carping demon at 9:25 PM on June 1, 2014

*This seems like...not a bad way to approach math to me? Isn't a huge part of math literacy being able to interpret which values in a problem are relevant and how to combine those values to solve some sort of...you know...problem? Being able to gather or interpret a set of values, pick out the two or three that will help you discern some previously unknown information, and then choosing the correct method out of the many you know to yield a useful answer that you didn't have before strikes me as actually a pretty sophisticated set of mathematical skills and not evidence that a bunch of 12-year-olds are mindless automatons.*

The phenomenon that the teacher seems to be upset with, based on what I see teaching math at the post-secondary level, is students who don't think to or know how to do the gather information, decide what information is relevant, choose a relevant method based on context, and interpret the result steps unless a problem is set up for them very carefully in exactly the same way as some other example problems that they have seen. Students who completed the probability exercise described without asking for a right answer were doing all of this.

I understand some of the reasons why it doesn't happen - it seems that my students get more and more anxious every year about their grades and about getting the university credential for getting a job afterwards. And with some reason - that bachelor's degree is now a pre-requisite for any sort of financially secure future job or career, but now far from a guarantee of such. But a lot of it is also how we talk about education and what formal education (i.e. school) is for (increasingly, we talk about it as a private good, providing job training and credentials; rather than as either a public good, providing an informed and critical democratic populous; or as something that helps individuals develop their full potential as human beings, as a transformative experience); and pressures put on younger and younger students by parents and teachers, pressures put on teachers and schools by testing and accountability metrics, etc. Students are told, often and strongly, that grades are important. And, unfortunately, this can be incommensurate with critical thinking and serious learning, since learning often requires taking intellectual risks (making guesses and mistakes, learning how to evaluate one's own level of knowledge, learning to trust one's own intellectual abilities rather than always seeking external evaluation), which are, you know, risky. Kids aren't born caring about or inclined to worry about arbitrary grades though, that's something that we teach them. Kids are generally born with a great deal of curiosity, a desire to try new things on their own and gain independence, the ability to form (strong) opinions about whatever problems or puzzles they encounter, and some basic reasoning ability. I haven't read or watched the TED talk of Ken Robinson yet, but from what I read about him/his works and talks, he seems to argue that much of what passes for formal schooling specifically teaches kids not to care about this sort of stuff, in addition to teaching them to worry about grades and credentialing. So the question of who trains the curiosity and independence out of kids and why seems quite reasonable to me.

posted by eviemath at 9:32 PM on June 1, 2014 [19 favorites]

@Snarl Furillo:

True. I dabble in the Yahoo! Answers math section (it occasionally has interesting problems) and I get the impression that this side of things isn't taught well in US schools. A very high proportion of Y!A math questions involve students being unable to convert "word problems" into equations.

posted by raygirvan at 9:57 PM on June 1, 2014

*Isn't a huge part of math literacy being able to interpret which values in a problem are relevant and how to combine those values to solve some sort of...you know...problem?*True. I dabble in the Yahoo! Answers math section (it occasionally has interesting problems) and I get the impression that this side of things isn't taught well in US schools. A very high proportion of Y!A math questions involve students being unable to convert "word problems" into equations.

posted by raygirvan at 9:57 PM on June 1, 2014

And that day, the kids learned that the right answer is to make your teacher think she's changing your life.

posted by michaelh at 10:05 PM on June 1, 2014 [25 favorites]

posted by michaelh at 10:05 PM on June 1, 2014 [25 favorites]

I think my main objection, now that I'm a wee bit calmer, is to the idea of an adult asking a room full of children why they were "broken." I mean, just imagine that situation from the perspective of a child in school. Imagine that you are a child, and an adult looks at you and says, "You're broken." Try to put yourself in that child's shoes- there you are, in school, trying to do the work your teacher has assigned you, trying to do it correctly, and this so enrages your teacher that she stops everything and says, "Who broke you?" It's a gotcha question a la "When did you stop beating your wife?" It doesn't allow for the answer, "I'm not broken at all." You don't even have to

I thought maybe I was overreacting and the author had just used the "broken" frame in the essay to paraphrase a discussion she had that was more "Why do you approach math this way" but her phrasing is pretty narrow:

I think that's part of the "renegade teacher" narrative that I hate- the idea that, by just giving the right answers, students are proving that they are naive rubes who need to be broken out of the matrix. Learning how to give the right answer in school is a skill, it's adaptive as fuck, and it's often the only way to win. Playing the game doesn't make you stupid, it just makes you a player.

posted by Snarl Furillo at 10:06 PM on June 1, 2014 [32 favorites]

*infer*your brokenness from something slightly less hateful! It's*right there in the premise.*I thought maybe I was overreacting and the author had just used the "broken" frame in the essay to paraphrase a discussion she had that was more "Why do you approach math this way" but her phrasing is pretty narrow:

*"In fact I am so desperate that*" I'm sure this isn't an exact transcript of how things went down- I mean, I hope a veteran teacher would have enough sense not to tell her students they were broken- but it sounds really, really mean. I mean, even if the kids ARE too focused on the right answer, that isn't some crazy stupid kid thing they dreamed up that they need to be snapped out of. It's smart as hell. They figured out what is expected of them in school like 90% of the time. Don't hate the player, hate the game.**I stopped class today to ask them who broke them**. Was it their parents, a former teacher, society, our education system or me that took away their inquisitive nature and made math only about getting a right answer?...Things went so much better the second time around with**not one student asking me if their answer was “right” (perhaps out of fear of another Powers meltdown).**I think that's part of the "renegade teacher" narrative that I hate- the idea that, by just giving the right answers, students are proving that they are naive rubes who need to be broken out of the matrix. Learning how to give the right answer in school is a skill, it's adaptive as fuck, and it's often the only way to win. Playing the game doesn't make you stupid, it just makes you a player.

posted by Snarl Furillo at 10:06 PM on June 1, 2014 [32 favorites]

eye of newt: "

The mindset of 'Getting the right answer' can be awfully useful though, even when the person giving the problem doesn't know what it is. I don't have my citations handy, but I recall reading that people spend more time on problems when they think there's a right answer. So asking a developer 'Is there a bug in this feature branch?' may trigger different behaviors than question than 'Can you find the bug in this branch?', and lead to higher quality code.

posted by pwnguin at 10:16 PM on June 1, 2014 [2 favorites]

*I work in engineering design and if our group just went for the first design that seemed to solve the industry's problems, our competitors would be eating our lunch. By trying to solve future problems, you can keep ahead. But what are the future problems? There's no right answer. There are only intelligent guesses, creativity, and luck.*"The mindset of 'Getting the right answer' can be awfully useful though, even when the person giving the problem doesn't know what it is. I don't have my citations handy, but I recall reading that people spend more time on problems when they think there's a right answer. So asking a developer 'Is there a bug in this feature branch?' may trigger different behaviors than question than 'Can you find the bug in this branch?', and lead to higher quality code.

posted by pwnguin at 10:16 PM on June 1, 2014 [2 favorites]

She sounds like a great teacher, but I can't believe she asked that seriously. I learned that math was only about the right answer at school 30+ years ago. Anyway kudos to her, sounds like an interesting exercise with some great discussions. I hated maths in school, because it always seemed so pointless. Now when I run into maths problems at work and in everyday life, I realise how interesting and creative it can be.

posted by Joh at 10:24 PM on June 1, 2014

posted by Joh at 10:24 PM on June 1, 2014

I've read this twice and I still don't really get it. Did the teacher tell the kids that

Because if not, this:

seems rather disingenuous. Of course 11- and 12-year-old kids don't expect maths to have this level of nuance or subjectivity, because that's not the way it's taught.

So your answer is: the education system 'broke the kids'. If, in fact, you believe they're broken. (I'm secretly wondering if your teaching methodology is broken.)

posted by Salamander at 10:28 PM on June 1, 2014

*there is no one right answer*before they started the exercise?Because if not, this:

*We talked about the need for them to stop worrying about if I think their answer is right and to start worrying about whether or not they thought their answer was right.*seems rather disingenuous. Of course 11- and 12-year-old kids don't expect maths to have this level of nuance or subjectivity, because that's not the way it's taught.

So your answer is: the education system 'broke the kids'. If, in fact, you believe they're broken. (I'm secretly wondering if your teaching methodology is broken.)

posted by Salamander at 10:28 PM on June 1, 2014

I'm clearly heavily biased, based on my own lived experience. I didn't give half a damn about math when I was 11, but at 31 am currently finishing up my Ph.D. in physics. I really appreciate the exercise that the teacher laid out for the students, as it seems fun and really educational, but I can also see a non-zero sum of students not caring about anything more than finishing their lesson so that they can go to lunch and recess. Just to be clear, I'm not trying to discount above statements that say that 11 year-olds are curious, intelligent, responsible kids. I'm sure that this is true, but I also think that children who don't care much about math, or just want to make it through the class, aren’t necessarily "broken." Again, it would be nice to have students gobbling up math like hungry puppies and then begging for more. As a scientist,

This is not to say that I disagree the teacher's dedication. I just take issue with the teacher's apparent belief that deviations from her own personal narrative, where everyone engages with all the necessary skills and interest, is evidence of broken children. I just can't agree with that.

posted by Shouraku at 10:28 PM on June 1, 2014 [4 favorites]

*I would love to see that*, but I also think if you view disinterest or bare-minimuming in a 7th grade math class as evidence that the children are "broken," then you may have been expecting a little too much out of them to begin with.This is not to say that I disagree the teacher's dedication. I just take issue with the teacher's apparent belief that deviations from her own personal narrative, where everyone engages with all the necessary skills and interest, is evidence of broken children. I just can't agree with that.

posted by Shouraku at 10:28 PM on June 1, 2014 [4 favorites]

*Trying to convince students to worry about things other than "the right answer" when the system is designed to make their future success hugely dependent upon getting "the right answer" is absurd and idiotic. You wrote the rules of this game and you should expect students to try to win it.*

It's an asymmetrical game at it's core: The students are playing the 'get a good grade' game, and the teacher is (hopefully) playing the 'instil some critical thought and a respect for the subject' game. The teacher (at least at university) has a bit of leeway in doing the game design, though. I try to arrange my courses to force the students to play my game if they want to win at their game.

posted by kaibutsu at 10:33 PM on June 1, 2014 [3 favorites]

*So I decided to try teaching information theory and complexity theory as a "humanities class".*

Information Theory: Claude Shannon's critical deconstruction of "The Prisoner" including a fully worked out system for calculating a Number for every resident of The Village.

posted by save alive nothing that breatheth at 10:38 PM on June 1, 2014 [1 favorite]

I'm a teacher. I think kids need to focus more on processes than answers. But it's really hard to see how this is evidence of anything other than the teacher's failure to scaffold the students' skills so that they could engage with the task the way she wants them to.

And having a meltdown about how they're doing it wrong probably isn't the best response, either.

posted by robcorr at 10:40 PM on June 1, 2014 [3 favorites]

And having a meltdown about how they're doing it wrong probably isn't the best response, either.

posted by robcorr at 10:40 PM on June 1, 2014 [3 favorites]

Saxon Kane:

We probably can't get anywhere until we stop using these pointlessly silly terms. "STEM" is a nonsense word with no cohesive meaning; it apparently refers to "science, technology, engineering, math," but these things have almost nothing to do with each other on an immediate basis. I too could invent such words: "LAP" for "literature, architecture, physics," maybe, or "DUM" for "drafting, underwriting, and manuscripts." Three or four things are bound to have

Science and mathematics are

The term "STEM" seems to derive from this petty notion we've adopted nowadays of a specialization that crowds out everything else. "STEM" people are geeks or techies or something like that; we like them because they do our research for us and build stuff for us, or at least that's what we vaguely assume as we wave out hands toward the internet and cell phones and stuff: "y'know,

The Liberal Arts are a cohesive whole, and they form the only true education, a liberal education - that is, quite literally, an education which liberates. A computer scientist who knows some math but nothing about literature or philosophy has not been liberated, has not been given access to the breadth of the ways humans have of approaching reality. A so-called professional philosopher who knows nothing about mathematics or science has not been liberated, either. We might not all become experts, but education at least means learning what expertise in these fields is, and that means getting our hands dirty and getting acquainted with them by forcing ourselves to try to understand them at least a little bit.

As long as we see education in terms of categories like "STEM" and "humanities," we will not appreciate the breadth of what true education - liberal education - can and must be. And we will suffer for it.

posted by koeselitz at 11:11 PM on June 1, 2014 [39 favorites]

*"So, maybe instead of trying to make the humanities more like STEM, we should make STEM more like the humanities?"*We probably can't get anywhere until we stop using these pointlessly silly terms. "STEM" is a nonsense word with no cohesive meaning; it apparently refers to "science, technology, engineering, math," but these things have almost nothing to do with each other on an immediate basis. I too could invent such words: "LAP" for "literature, architecture, physics," maybe, or "DUM" for "drafting, underwriting, and manuscripts." Three or four things are bound to have

*some*relationship, but that doesn't make it sensible to smash them together as a purported discipline.Science and mathematics are

*Liberal Arts*. That is what they've always been, just like logic and literature. They are "Liberal Arts" because they make free human beings out of creatures who are normally slaves to their dogmatic beliefs, slaves to the things they were taught by their parents, slaves to their desires or their circumstances. The Liberal Arts are a cohesive education. They are not the core of an education or a useful add-on to an education; they*are*what a cohesive education is. Education means freeing people, freeing people in the deepest sense - to think for themselves - and the only way to do so is to give them training in mathematics, in science, in literature, in philosophy, in music.The term "STEM" seems to derive from this petty notion we've adopted nowadays of a specialization that crowds out everything else. "STEM" people are geeks or techies or something like that; we like them because they do our research for us and build stuff for us, or at least that's what we vaguely assume as we wave out hands toward the internet and cell phones and stuff: "y'know,

*STEM.*" And since we don't want people who like things like literature to feel left out, we repurposed this old term "humanities" to mean "anything people study in school that isn't STEM or law or medicine or practical like that." And then we're surprised that "humanities" are more and more marginalized.The Liberal Arts are a cohesive whole, and they form the only true education, a liberal education - that is, quite literally, an education which liberates. A computer scientist who knows some math but nothing about literature or philosophy has not been liberated, has not been given access to the breadth of the ways humans have of approaching reality. A so-called professional philosopher who knows nothing about mathematics or science has not been liberated, either. We might not all become experts, but education at least means learning what expertise in these fields is, and that means getting our hands dirty and getting acquainted with them by forcing ourselves to try to understand them at least a little bit.

As long as we see education in terms of categories like "STEM" and "humanities," we will not appreciate the breadth of what true education - liberal education - can and must be. And we will suffer for it.

posted by koeselitz at 11:11 PM on June 1, 2014 [39 favorites]

*High school algebra would have been so much easier and better if the oh-so-boring Mrs. Stark had explained why we were expected to commit the quadratic formula to memory.*

I've never understood that either. If, later in life, I should ever have any call for the quadratic formula (hey, it could still happen; it's only been 15 years since high school), am I still not allowed to look it up?

Solely because of that stupid, pointless rule, I failed high school math -- the easy track, colloquially called "trucker math" -- at least once if not twice, and consequently anything STEM has been strictly off-limits ever since.

Hell yes, the right answers are what matters in school. Wrong answers fuck up the rest of your life. It shouldn't be that way, but that it is is not a problem with the students.

posted by Sys Rq at 11:15 PM on June 1, 2014 [4 favorites]

I was an accelerated student across the board until 8th grade math. The teacher was a relatively nice guy and lots of kids loved him, but I couldn't get anything out of his explanations. And then he put it all on me for not putting in enough effort. I only managed a C in his class by showing up for lots of extra practice time before & after school in his classroom... where he never helped me at all. That was the point where I went from being a "gifted" student to a math dummy, all until college.

And twenty-five years later, as a teacher myself, I'm still chewing on where that breakdown was. My jr. high brain chemistry? His teaching style? Simple crossed wires in ordinary human communication? I don't remember ever really

I dunno. But whenever I substitute in a middle school math class and I look at the textbook and the exercises -- even for things I genuinely understand now -- I can't for the life of me understand how in the hell anyone thinks a kid is gonna learn anything from the way those books are written and the examples they give.

posted by scaryblackdeath at 11:33 PM on June 1, 2014 [2 favorites]

And twenty-five years later, as a teacher myself, I'm still chewing on where that breakdown was. My jr. high brain chemistry? His teaching style? Simple crossed wires in ordinary human communication? I don't remember ever really

*learning*much, just a whole lot of endless*displays of effort.*And, yeah, I really, really just wanted to get the answer right, because if I could do that, then that meant I understood the concept and how it worked.I dunno. But whenever I substitute in a middle school math class and I look at the textbook and the exercises -- even for things I genuinely understand now -- I can't for the life of me understand how in the hell anyone thinks a kid is gonna learn anything from the way those books are written and the examples they give.

posted by scaryblackdeath at 11:33 PM on June 1, 2014 [2 favorites]

*And that day, the kids learned that the right answer is to make your teacher think she's changing your life.*

Ugh. For all too many teachers, yeah. Last apprentice teacher I worked with was clearly going into teaching to salvage her sense of self-worth after a nasty divorce. I kept looking for ways to say, "Hey... working with teenagers is

*not*going to make you feel better about yourself. Come at it looking for that, and they'll just chew you up." But by that point, she'd walked away from a laboratory job doing actual science (as opposed to teaching it), and she'd coughed up the money for her credential and her masters, so what else was she going to do?

Funny enough, most of the young lawyers I've known go through a similar process. :(

posted by scaryblackdeath at 11:39 PM on June 1, 2014

As the Mars Climate Observer showed, getting the right answer really isn't the most important thing.

posted by happyroach at 12:04 AM on June 2, 2014 [1 favorite]

posted by happyroach at 12:04 AM on June 2, 2014 [1 favorite]

Whoever broke these kids parents first?

google results for 40 percent of Americans believe

posted by C.A.S. at 1:11 AM on June 2, 2014

google results for 40 percent of Americans believe

posted by C.A.S. at 1:11 AM on June 2, 2014

52 times? Teachers should keep in mind the possibility that pupils are winding them up.

posted by Segundus at 1:18 AM on June 2, 2014 [2 favorites]

posted by Segundus at 1:18 AM on June 2, 2014 [2 favorites]

The problem with the above task is that if you look closely at all the items to be placed on the probability line there is in fact a "correct" place to put most of them.

And even for the subjectively evaluated ones there are places that are more "correct" than others. So I don't think there is anything surprising that children would want to make sure that they have performed the task correctly and correctly interpreted all the subjective statements.

posted by mary8nne at 1:41 AM on June 2, 2014 [2 favorites]

And even for the subjectively evaluated ones there are places that are more "correct" than others. So I don't think there is anything surprising that children would want to make sure that they have performed the task correctly and correctly interpreted all the subjective statements.

posted by mary8nne at 1:41 AM on June 2, 2014 [2 favorites]

*For real tho I still am not sure about the weather. If it said on the news last night there is a 60% chance of rain today, but it doesn't rain, doesn't that mean there was actually a 0% chance of rain?*

The usual formal definition of probability is what you'd call the objectivist or frequentist sort, where you define it to be the relative amount of some total number of repetitions of something that fit whatever, so the probability of a die coming up 6 is the total number of times a die comes up 6 out of all the times it is rolled. For events of the sort you can sensibly come up with such a probability, it's basically the proportion of events 'in the long run'.

Now it turns out that if you try to come up with a system of assigning your level of belief in something to a number, and apply some fairly straightforward and obvious requirements to how that should work, you find that any system you use must be easy to translate to one that uses numbers between 0 and 1 and obey all the other expected rules of probability. Additionally, if you asked me how much I believe a die will come up 6 or whatever, it seems perfectly sensible to answer '1/6', so you can generalise probability to something that turns out to act like a level of belief in a proposition. This is spelled out in The Algebra of Probable Inference, by Richard Cox. Be warned, this is a mathematical book and not light reading, although it is a slim volume. Bayesians treat probability in this way, although it is not perhaps directly related to Bayes Theorem - it's just that once you start down this road you'll end up using that theorem a lot.

So once you've gone to that - a subjectivist idea of probability - it's perfectly easy to talk about probabilities for events that can happen only once. What should be the case though, is that if you ask me all sorts of questions about whatever you like where I give probabilities of answers, the number of times I'm right about questions where I reply "60%" should be about 60%. In practice, nobody is perfect, but it's what I might aspire to. Likewise it is what the weather forecaster should aspire to.

From a historical point of view, people have been treating probabilities like this for a long time. One notable early example was Pierre Laplace, who spoke about the mass of Saturn being within a certain range with certain odds. Of course the mass of Saturn is fixed (ignoring accumulation of other small objects and that sort of thing - the speed at which it changes is so small that it's essentially fixed), so it makes no frequentist sense to talk of a probability of it being within some range. It's either right or it's wrong. But that didn't stop Laplace.

So, it's perfectly reasonable for one weather forecaster to say "there's a 60% chance of rain today" and another one to say "there's a 90% chance of rain today", because they might be using subjectivist probability, and that's as the name suggests rather subjective. But this is all a rather philosophical issue on the nature of probability, and for the purposes of a mathematics class at this level I'd expect you to be teaching an objectivist definition first, and hope you don't have to go into this sort of subtlety. Here's the wikipedia article on the subject, and I have no idea how you'd go about explaining that to your typical schoolkid. I imagine it would be totally soul-destroying if this sort of thing was in your first introduction to probablity, especially if presented with any sort of formality.

posted by edd at 2:57 AM on June 2, 2014 [5 favorites]

*Poor kids are bad at school, rich kids are good at school, amirite?*

Yes, that's what I meant in my comment above.

Notice I didn't say "rich kids are more intelligent" or "rich kids have more innate capability."

What we're talking about is the ability to do well at "school" (doing well at school isn't always an advantage, as any indepted, unemployed PhD will tell you).

Children who come from families where the parents do well at school are generally going to do better at school. The parents know how to play the game of school.

There's also home environment. If you did not have breakfast or don't have a good lunch, are you going to do well at school? If your parents cannot afford books (or perhaps are not as inclined to buy them), will you do as well at school as students from a more affluent cohort?

The answer is you will not.

posted by KokuRyu at 3:02 AM on June 2, 2014 [5 favorites]

The one phrase common to every math class I ever took took was "show your work". Full credit was not given for the correct answer without showing your work. Is that no longer the case?

posted by klarck at 3:05 AM on June 2, 2014 [1 favorite]

posted by klarck at 3:05 AM on June 2, 2014 [1 favorite]

I was reminiscing yesterday about a class in social science theory I took in college. I think it was the first time I truly was asked to engage in critical thinking. That didn't come easy but the class was a discussion seminar, the professor was a patient, wise man, and by the end of the semester I'd grown intellectually - and I knew it, although I couldn't articulate exactly how at the time, or what was missing before.

So... that was COLLEGE, and that was 30 years ago. I'm not sure that public high school education in the States was ever intended to produce critical thinkers: if it did, it was probably an accident or some hippie teacher throwing wrenches into the conformist factory's machines. Kids who press a lever looking for the right answer? Expected outcome.

posted by Sheydem-tants at 3:09 AM on June 2, 2014

So... that was COLLEGE, and that was 30 years ago. I'm not sure that public high school education in the States was ever intended to produce critical thinkers: if it did, it was probably an accident or some hippie teacher throwing wrenches into the conformist factory's machines. Kids who press a lever looking for the right answer? Expected outcome.

posted by Sheydem-tants at 3:09 AM on June 2, 2014

I broke them.

posted by Lipstick Thespian at 3:19 AM on June 2, 2014 [1 favorite]

posted by Lipstick Thespian at 3:19 AM on June 2, 2014 [1 favorite]

In my teaching experience, if students are asking 52 times if their answers are right, they're highly successful at

Either the expectation wasn't made clear to them (and if they're asking that many times, it would seem that it was a poorly taught lesson), or they're just not engaged by the lesson and they know a great way to get Ms. Powers to stop math is to keep bugging her and ask, "Is this right?"

Either way, if I knew one of my teachers asked the students who broke them, she would be in serious trouble. Jesus. Telling students they're

posted by kinetic at 3:22 AM on June 2, 2014 [3 favorites]

**getting the teacher to end the lesson.**Either the expectation wasn't made clear to them (and if they're asking that many times, it would seem that it was a poorly taught lesson), or they're just not engaged by the lesson and they know a great way to get Ms. Powers to stop math is to keep bugging her and ask, "Is this right?"

Either way, if I knew one of my teachers asked the students who broke them, she would be in serious trouble. Jesus. Telling students they're

**broken?**posted by kinetic at 3:22 AM on June 2, 2014 [3 favorites]

Hang on. If 80% of the stream is less than three feet deep, then my chances of getting across without drowning are eight in ten?

Tell me again, why should I learn to set up a word problem?

Please don't tell the children they are broken.

posted by mule98J at 3:30 AM on June 2, 2014

Tell me again, why should I learn to set up a word problem?

Please don't tell the children they are broken.

posted by mule98J at 3:30 AM on June 2, 2014

I've never been a proper K-12 teacher, although I have tutored and taught in an after school program, and I sort of subscribe to the belief that non-teachers should shut up about teaching. But I work with first year college students, and I can sort of see where she's coming from. My students' problem isn't exactly that they want to get the right answer. It's that they want to e given steps to get to the right answer without doing the hard work of mastering the concepts. They're also a little scared of being confused or wrong, which makes it harder to master concepts. I wouldn't say they're broken, but I wish they were encouraged to be more comfortable with taking risks and making mistakes.

posted by ArbitraryAndCapricious at 4:04 AM on June 2, 2014 [4 favorites]

posted by ArbitraryAndCapricious at 4:04 AM on June 2, 2014 [4 favorites]

What Snarl said, times a billion. Teachers can't just wing it in the classroom; careful planning needs to be done to get the outcome you want. But you have to know what it is you

Teaching is hard, people.

posted by zardoz at 4:52 AM on June 2, 2014 [1 favorite]

*want*.Teaching is hard, people.

posted by zardoz at 4:52 AM on June 2, 2014 [1 favorite]

Yes, well, once you convert your entire education system into a job-training machine, how can it

posted by Thorzdad at 4:53 AM on June 2, 2014 [4 favorites]

*not*become all about focusing on getting the right answer? We fire poor performers (dead weight, not a good fit, not team players, etc) who don't get things right 110% of the time.posted by Thorzdad at 4:53 AM on June 2, 2014 [4 favorites]

*My students truly believe for some reason that math is about combining whatever numbers you can in whatever method that seems about right to get one “answer” and then call it a day.*

So I was taught in a very postwar/engineering-track style of math (ie, never exposed to set theory or any probability or statistics until college), but I don't know that it's possible for 7th-8th grade math to be about anything

*other*Than THE answer.

I never really understood (as in, fully grasped the 'why') anything about math until Calculus my senior year in high school. And I have a hard time seeing how, say, algebra can be about anything other than being taught How To Do It, and checking answers.

Maybe this is what Common Core is trying to address, and maybe it's different in a Montessori-like setting. But these kids being 'broken' doesn't sound new to me at all. And it might just be a function of how math works, in that you can't really see what's going on behind the curtain until you spend a decade seeing what's going on onstage.

posted by graphnerd at 5:58 AM on June 2, 2014

My rule of thumb is that if

posted by xigxag at 6:06 AM on June 2, 2014 [3 favorites]

*the whole rest of the world*seems to have a problem, I try to at least consider the possibility that maybe it's*me*with the problem.posted by xigxag at 6:06 AM on June 2, 2014 [3 favorites]

In English class 7th grade I wrote up a book report stating that Boo Radley was the antagonist and the teacher marked it wrong.

Look it's not the

Also: learning to think outside the box is a process; these kids won't develop those skills if the first time they 'fail' your teaching exercise, you take to the internet to bitch about it.

posted by St. Peepsburg at 6:20 AM on June 2, 2014 [1 favorite]

Look it's not the

*traditional*answer, but he did scare those kids for a few summers.Also: learning to think outside the box is a process; these kids won't develop those skills if the first time they 'fail' your teaching exercise, you take to the internet to bitch about it.

posted by St. Peepsburg at 6:20 AM on June 2, 2014 [1 favorite]

I suppose there is no turning back. By next February, the titles of more than 98.5% of all blog posts/articles/news stories will be formulated as a rhetorical question, I'm almost certain of it.

posted by Walleye at 6:39 AM on June 2, 2014

posted by Walleye at 6:39 AM on June 2, 2014

Having never taken psychology classes, perhaps this is a well understood phenomenon, but it seems to me that there is great appeal in the idea that there is just "right" and just "wrong" in the world, and perhaps there is some point in development when a person is able to set aside those fixed positions and see more facets to an issue.

Then again, I'm not sure most people reach that greater understanding outside of some narrow area of their profession or interest.

To show an example: two reasonably educated people debate climate change. Neither one is a scientist, but both use "science" as their main argument. The climate change denialist points to his selected reports and studies, and his opponent the same. Neither one actually possesses the deeper understanding to analyze the science. They could read and regurgitate, or rely on their favorite news sources to do so for them. They effectively reduce the argument to a "he said, she said" stalemate.

posted by fontophilic at 6:43 AM on June 2, 2014

Then again, I'm not sure most people reach that greater understanding outside of some narrow area of their profession or interest.

To show an example: two reasonably educated people debate climate change. Neither one is a scientist, but both use "science" as their main argument. The climate change denialist points to his selected reports and studies, and his opponent the same. Neither one actually possesses the deeper understanding to analyze the science. They could read and regurgitate, or rely on their favorite news sources to do so for them. They effectively reduce the argument to a "he said, she said" stalemate.

posted by fontophilic at 6:43 AM on June 2, 2014

Benito StruassAtlanta public schools info.

Lots of titles, few seem to be " teacher."

posted by Ideefixe at 7:06 AM on June 2, 2014

Lots of titles, few seem to be " teacher."

posted by Ideefixe at 7:06 AM on June 2, 2014

I completely emphasize with this teacher. Her exercise sounds ambituous, but if the skills were there (they'd been taught numberlines, fractions, probability, percents, and the meaning if words like "certain" and "likely") it's a very reasonable exercise. I would given it to them as a group exercise with a giant number line and let students pick what they wanted to pin and given feedback for each choice, or at the very beginning of the unit with *written instructions* that they would only be graded for trying (because kids don't listen to oral instructions).

But trying something new and getting a meltdown and feeling horrified that the reaction to a challenge was a meltdown, I totally understand. The other day I asked students to compare the probabilties they had calculated for rolling a die and getting (an odd number, a prime number, etc) - which we had already checked as a class - with the number of times they actually got that outcome - basically, to compare two fractions in a chart. I gave them the chart to fill out and told them I would count it "as a quiz grade" but they could work together and I'd help them. The kids heard "quiz", saw that it wasn't exactly the same as something we'd already covered in that class, and freaked out hardcore. I then had to reteach the entire lesson again the next day after first reteaching them how to compare two fractions (which I had been hoping they would pick up from each other or ask me about, since these kids are already in 10th grade).

These are kids who aren't good at math, but the bigger problem (the reason they aren't good at math) is that they wait to be shown *exactly* how to do a problem, and then apply exactly what they have seen to the same problem 20 times. They then immediately forget what they have "learned" since they didn't understand any if of it in the first place.

(They also expect to not do any work on Fridays and to only "learn" one thing each day, which must be somthing they can pick up in five minutes and practice for an hour.)

I hear "but we can do it after you show us how" a lot from them - thry don't understand that math isn't just applying formulas you have been shown that day to identical problems.

If the students have the skills but don't know how to put them together, absolutely they should have lessons about how to do that. It's a crucial skill for math.

posted by subdee at 7:06 AM on June 2, 2014 [7 favorites]

But trying something new and getting a meltdown and feeling horrified that the reaction to a challenge was a meltdown, I totally understand. The other day I asked students to compare the probabilties they had calculated for rolling a die and getting (an odd number, a prime number, etc) - which we had already checked as a class - with the number of times they actually got that outcome - basically, to compare two fractions in a chart. I gave them the chart to fill out and told them I would count it "as a quiz grade" but they could work together and I'd help them. The kids heard "quiz", saw that it wasn't exactly the same as something we'd already covered in that class, and freaked out hardcore. I then had to reteach the entire lesson again the next day after first reteaching them how to compare two fractions (which I had been hoping they would pick up from each other or ask me about, since these kids are already in 10th grade).

These are kids who aren't good at math, but the bigger problem (the reason they aren't good at math) is that they wait to be shown *exactly* how to do a problem, and then apply exactly what they have seen to the same problem 20 times. They then immediately forget what they have "learned" since they didn't understand any if of it in the first place.

(They also expect to not do any work on Fridays and to only "learn" one thing each day, which must be somthing they can pick up in five minutes and practice for an hour.)

I hear "but we can do it after you show us how" a lot from them - thry don't understand that math isn't just applying formulas you have been shown that day to identical problems.

If the students have the skills but don't know how to put them together, absolutely they should have lessons about how to do that. It's a crucial skill for math.

posted by subdee at 7:06 AM on June 2, 2014 [7 favorites]

*For real tho I still am not sure about the weather. If it said on the news last night there is a 60% chance of rain today, but it doesn't rain, doesn't that mean there was actually a 0% chance of rain?*

No, it means there's a 0% chance it

*did*rain. Probability is about putting a reasonable measure on an uncertainty. Once whatever it is you

*were*uncertain about has happened and has been observed or measured or otherwise moved from not-yet-known to known, the new information you now have changes the probabilities involved.

Sometimes the way that probabilities shift in the light of new information is nowhere near as clear and obvious as the chance of rain shifting from 60% before that non-rainy day to 0% afterward (the Monty Hall Problem is a classic example).

People are notoriously bad at probability. Even some quite respectable thinkers have tied themselves into horrible conceptual knots with a problem that to me appears completely congruent with the 0%-chance-of-rain-after-the-fact scenario: starting from the (to me obviously spurious) premise that it's

*incredibly unlikely*for assorted physical constants to have the

*exact*values they do, people come up with all kinds of weird and convoluted explanations for how that might have happened.

This has long seemed to me exactly backwards: those constants form part of our best description of how things are, not some arbitrarily tweakable recipe for prescribing how things might possibly be. And yet you'll have no difficulty finding endless argument and speculation about

*why*the fine structure constant is what it is, and how utterly wondrous it is for it to have the one precise value that stops the Universe from having come out all broken and unworkable.

Yeah, well. Pardon me if I fail to be astonished that triangles have exactly

*three*sides instead of maybe two or four or five. Perhaps I am simply too broken to have much respect for wrong answers.

posted by flabdablet at 7:11 AM on June 2, 2014 [1 favorite]

KokuRyu:

John Roderick in his "Roderick on the Line" podcast has been touting a proposal for some time in which America's 13-year-olds spend a year cutting trails in the National Park System instead of attending school. Based on dealing with my 13-year-old's 7th Grade experience, it may be the best idea to hit education since the chalkboard.

posted by Rock Steady at 7:18 AM on June 2, 2014 [1 favorite]

*They are going through puberty and are learning more about how to interact socially. In some ways it may be a good idea to send them all to sports camp or something at age 13, and then bring them back to school at age 15 or 16.*John Roderick in his "Roderick on the Line" podcast has been touting a proposal for some time in which America's 13-year-olds spend a year cutting trails in the National Park System instead of attending school. Based on dealing with my 13-year-old's 7th Grade experience, it may be the best idea to hit education since the chalkboard.

posted by Rock Steady at 7:18 AM on June 2, 2014 [1 favorite]

This reminds me of the day in sixth grade when our art teacher decided to teach us some Mathematical Truth. He started quizzing us on some basic math problems, say maybe 6x8. We all shouted out 48, and he asked, "48 what?" I guess he was trying to get us to connect math to the real world rather than just some meaningless facts we memorized, but none of us had the slightest idea what he wanted from us. How the hell were we supposed to know what we had 48 of at the end when he hadn't told us what the 6 and 8 we were starting out with had been. He lectured us about how we important this was and kept trying to get his point through to us, but we just didn't get it. I was a great math student at the time, but all I learned that day was that I was too dumb to understand this basic concept. Rather than making a new connection in our little brains, he taught an entire class that we weren't very good at math.

To this day, I'm not sure if he really believed he had an important point that he just wasn't able to get across to us because . . . art teacher, or if he was just messing with us. He did have a very dry and odd sense of humor, so that's entirely possible.

This teacher appears to have been more successful than Mr. Montee was with us, but one day out of the blue teaching kids that they have been thinking about math all wrong up until that very minute and that they have to change it right now doesn't seem like the best approach to helping students feel more comfortable with math.

posted by Dojie at 7:19 AM on June 2, 2014 [2 favorites]

To this day, I'm not sure if he really believed he had an important point that he just wasn't able to get across to us because . . . art teacher, or if he was just messing with us. He did have a very dry and odd sense of humor, so that's entirely possible.

This teacher appears to have been more successful than Mr. Montee was with us, but one day out of the blue teaching kids that they have been thinking about math all wrong up until that very minute and that they have to change it right now doesn't seem like the best approach to helping students feel more comfortable with math.

posted by Dojie at 7:19 AM on June 2, 2014 [2 favorites]

**Flabdablet**: Well, the Monty Hall problem provides an excellent example of subjectivist probability at work. You think there's a 1/3 chance there's a car behind door A, but Monty might think there's a 0 chance there's a car behind door A, because he already knows where it is. Are you both right, or is only Monty right? There are those that think only Monty is right, although they are totally fine with the idea of using the available information to them to make a suitably informed choice about where to place their bets. And as I said above, while I think I'd have a challenging time doing this teacher's job ordinarily, I'd hate to also have to explain to them why two students can both be right about an estimate of a probability for it to rain tomorrow being 60% and 90%, yet still tell them there's only one right answer to question 3 on the test paper I just set them.

posted by edd at 7:46 AM on June 2, 2014

I hope I never have to work with people who learned that math isn't about getting the right answer.

Of course it is. That's what makes it useful.

That doesn't mean that we should be teaching math by rote, or that kids shouldn't be encouraged to

All of those things are fine and good and we need more of them. But nothing about them suggests that getting the right answer is unimportant.

posted by escape from the potato planet at 7:57 AM on June 2, 2014 [2 favorites]

Of course it is. That's what makes it useful.

That doesn't mean that we should be teaching math by rote, or that kids shouldn't be encouraged to

*understand*the mathematics they're doing, on a deeper level than "pull lever A, push button B, turn knob C, get the answer", and apply that understanding creatively to solve problems.All of those things are fine and good and we need more of them. But nothing about them suggests that getting the right answer is unimportant.

posted by escape from the potato planet at 7:57 AM on June 2, 2014 [2 favorites]

I wonder if this anecdote comes from a mixed-ability class or a calculators-banned class, each of which is a devastatingly stupid way to teach seventh graders. Properly tracked, you can have a robust theoretical discussion of math relevant to each ability level, with a strong organic connection to the proper algorithms. With calculators allowed, you can naturally focus on theory because the kids aren't going to be stuck on the arithmetic.

posted by MattD at 7:57 AM on June 2, 2014 [1 favorite]

posted by MattD at 7:57 AM on June 2, 2014 [1 favorite]

Who or what broke this teacher?

What, pray the fucking tell, is the difference between "sometimes correct and sometimes not" and

posted by kanewai at 9:17 AM on June 2, 2014 [1 favorite]

*Things went so much better the second time around with not one student asking me if their answer was “right” (perhaps out of fear of another Powers meltdown). For the first time I heard some really rich discussions that were sometimes correct and sometimes were not but the important thing was the kids were talking about the math.*What, pray the fucking tell, is the difference between "sometimes correct and sometimes not" and

*right*and*wrong*?posted by kanewai at 9:17 AM on June 2, 2014 [1 favorite]

*You think there's a 1/3 chance there's a car behind door A, but Monty might think there's a 0 chance there's a car behind door A, because he already knows where it is. Are you both right, or is only Monty right?*

Both are as right as it's possible to be, given the information available to each.

posted by flabdablet at 9:32 AM on June 2, 2014 [1 favorite]

She's not saying that there's no such thing as a right answer. She's saying that you can't learn math if you're only interested in getting to the right answer and not interested in grappling with mathematical concepts so you really understand how you arrived at that answer.

posted by ArbitraryAndCapricious at 9:33 AM on June 2, 2014 [5 favorites]

posted by ArbitraryAndCapricious at 9:33 AM on June 2, 2014 [5 favorites]

Jean Anyon wrote ‘Ghetto Schooling’, in it:

In the working-class schools, she found, work entailed the rote following of procedure, with no analytical thought encouraged. In the middle-class school, she wrote, “work is getting the right answer.”

In a more affluent school, Professor Anyon found, work emphasized creativity. In the wealthiest school, work meant “developing one’s analytical intellectual powers.”

These differences, she concluded, helped recapitulate existing class divisions. The children of blue-collar families, for instance, received “preparation for future wage labor that is mechanical and routine,” while those of wealthy families were taught skills that would help them assume leadership positions.

“Attempting to fix inner-city schools without fixing the city in which they are embedded,” she wrote in “Ghetto Schooling,” “is like trying to clean the air on one side of a screen door.”

I would say "attempting to fix kids without fixing the ENTIRE grade/'right answer' culture in which they are embedded is like trying to clean the air on one side of a screen door.

posted by lalochezia at 9:45 AM on June 2, 2014 [7 favorites]

*What Snarl said, times a billion. Teachers can't just wing it in the classroom; careful planning needs to be done to get the outcome you want. But you have to know what it is you want.*

Teaching is hard, people.

Teaching is hard, people.

It's also worth noting that

**a teacher does in a classroom, outside observers will often complain that they're doing it wrong. For instance, one might object to her calling her students "broken," but we don't know the tone of that classroom or the common language. That might be relatively harmless language... and yes, there may be one or two kids who might feel hurt by that comment, but there are also kids who'd take "Did you have a nice weekend?" the wrong way, too. You're dealing with anywhere from 20-35+ middle schoolers at a time. I guarantee you,**

*whatever**someone*is having an awful day or even an awful life, and that goes for rich kids as well as poor.

posted by scaryblackdeath at 10:00 AM on June 2, 2014 [1 favorite]

**flabdablet**: I agree with you, but there is a school that thinks we're wrong, and they're not really

*mathematically*wrong to say that. They've simply defined the word 'probability' more narrowly than us.

posted by edd at 10:28 AM on June 2, 2014

*there is a school that thinks we're wrong*

Then I shall give them a failing grade. Fear me.

posted by flabdablet at 10:30 AM on June 2, 2014

I dropped out of high school. Had I finished, had I graduated number one in my class, I'd still be in poverty today, washing dishes and cooking on the line, because I still wouldn't have the financial support to go to a 4-year, live on campus, not work full time. All this at the heart of a big spit structure of lies necessary for Grown Ups to tell and believe--"your future depends on how seriously you take your education!"--that unpalatable fact that money is absolutely required to go anywhere and do anything. Scholarships will always only get you n/n+1 the way there, there's still food clothes utilities laundry transportation bed to sleep on that implicitly gets payed for from your loving and financially able guardians. Part time jobs aren't sufficient income-supplements anymore, they are hard and low paying and if you're going to earn a living wage on your own as a young person, you must work full time, and it will be a hard living, and you will come to see the harsh reality that boom times and promises are long gone and you will feel angry at the system for telling you lies. I'm slowly making my way to a place where community college will be a feasible part of my schedule, but I'm happy to have dropped out, if anything because it represents how I feel about public education and the system negotiating what that phrase means.

I guess I'm reminded of this now because the essay by this teacher puts me back in a seventh grade classroom for a moment, feeling different from the kids around me who are off in college right now behaving themselves as they did back then, because they could--they had the privilege of a financially secure future in school, everything from class trips through Europe to buying a nice suit for the model UN conference to having the freedom to spend their new adult lives not scrubbing dishes but studying and doing homework and knowing they're accounted for. For those kids, the meaningless grind of grade school and beyond made sense, and so when a teacher asks what broke them, they don't internalize some special lesson, they see it as the Special Level in the game where teacher makes moral appeal and to beat the level you have to press x to cue somber response. Alright, next level. Insert token.

posted by Taft at 10:47 AM on June 2, 2014 [4 favorites]

I guess I'm reminded of this now because the essay by this teacher puts me back in a seventh grade classroom for a moment, feeling different from the kids around me who are off in college right now behaving themselves as they did back then, because they could--they had the privilege of a financially secure future in school, everything from class trips through Europe to buying a nice suit for the model UN conference to having the freedom to spend their new adult lives not scrubbing dishes but studying and doing homework and knowing they're accounted for. For those kids, the meaningless grind of grade school and beyond made sense, and so when a teacher asks what broke them, they don't internalize some special lesson, they see it as the Special Level in the game where teacher makes moral appeal and to beat the level you have to press x to cue somber response. Alright, next level. Insert token.

posted by Taft at 10:47 AM on June 2, 2014 [4 favorites]

Maybe she should take that as a sign that the students crave knowing whether they are correct when doing math, which is one of our precious few fields with strictly correct answers.

I had to suffer through math conversations and essays, which totally broke me when it came time to major in a very math-intensive major.

>If You Can Type the Problem into Wolfram Alpha and Get an Answer You Aren’t Doing Math

Actually, up until rigorous proof based courses, you ARE doing math. I am currently learning advanced integration and Differential equations, and for the first time in my life I have hit the point where Wolfram Alpha can't answer all the questions, because they are beyond the power of computation.

But in lower grades kids need to discuss their feelings in math less, and do more god**** worksheets. Less talking, less discussions, more algebra worksheets. More tests. More intense homework and studying. Let's get these kids great at math, and show them that there are correct answers, and that they can get them.

Let's not get together in a circle and discuss how probability makes us feel. That will only damage the kids who actually want to go on to do something rigorous, and does no favors to those who don't.

This reminds me of the Simpsons episode where the new teacher asks Lisa "How do numbers make you feel?"

posted by jjmoney at 12:00 PM on June 2, 2014 [2 favorites]

I had to suffer through math conversations and essays, which totally broke me when it came time to major in a very math-intensive major.

>If You Can Type the Problem into Wolfram Alpha and Get an Answer You Aren’t Doing Math

Actually, up until rigorous proof based courses, you ARE doing math. I am currently learning advanced integration and Differential equations, and for the first time in my life I have hit the point where Wolfram Alpha can't answer all the questions, because they are beyond the power of computation.

But in lower grades kids need to discuss their feelings in math less, and do more god**** worksheets. Less talking, less discussions, more algebra worksheets. More tests. More intense homework and studying. Let's get these kids great at math, and show them that there are correct answers, and that they can get them.

Let's not get together in a circle and discuss how probability makes us feel. That will only damage the kids who actually want to go on to do something rigorous, and does no favors to those who don't.

This reminds me of the Simpsons episode where the new teacher asks Lisa "How do numbers make you feel?"

posted by jjmoney at 12:00 PM on June 2, 2014 [2 favorites]

Why not design the lesson so that the teacher has already told the kids to do the *entire* assignment, centering on how they form their arguments, and that the "correct" answers will *only* be revealed to everybody at the end? The end would be more of a "of course the secret scroll was a mirror all along" sort of moment, and that would be more than okay.

posted by Sticherbeast at 12:10 PM on June 2, 2014

posted by Sticherbeast at 12:10 PM on June 2, 2014

*What, pray the fucking tell, is the difference between "sometimes correct and sometimes not" and right and wrong?*

The point is that that they're both valuable discussions.

*Let's not get together in a circle and discuss how probability makes us feel.*

I don't know if this is your actual understanding of what is being argued for or if it's an intentionally silly caricature, but it's a silly caricature either way. Maths is conceptual, and doing it well requires not only repetition and practice, although it certainly requires those, but also a conceptual understanding of what objectives are being aimed at and how the steps taken relate to them. It's not about how numbers make you feel, it's about what numbers actually mean and how they relate to each other and the world. Rigour is not simply about reproducing a result by following established steps, it's about being able to rearrange the steps or devise new steps, in order to achieve the desired result. That is conceptual rigour, and it's vital to mathematics, although merely incredibly useful for arithmetic

It seems possible that you are allowing your own difficulty with that aspect of mathematical rigour to colour your perception of its value.

posted by howfar at 12:18 PM on June 2, 2014 [3 favorites]

I have mixed feelings about this article: On the one hand, I like the discussion of reasoning very much. On the other, I'm worried this leads to "My opinion is as good as anyone else's, and better than most!" Much of math does have a "right" answer. What I think is missing is the idea that math is a creative endeavor.

posted by BillW at 12:50 PM on June 2, 2014

posted by BillW at 12:50 PM on June 2, 2014

To the people in this thread objecting to the "What broke you?" discussion, saying that it will damage the students' confidence in their abilities, that might be true, but it also might be true that not being able to think creatively on standardized tests (which *do* require creativity to complete, since they will not be exactly the same as what students have done in class, or at least they should not be exactly the same) will damage students' confidence in their abilities.... and also prevent them from moving on to the next [class/grade/school/life].

In my experience, the students would have enjoyed the chance to complain about their past math experiences, blame their old teachers or old school for their current predicament, and basically take a break for the day from actually doing math. It's not a bad thing to stop a disastrous lesson and have A Talk.

posted by subdee at 1:14 PM on June 2, 2014

In my experience, the students would have enjoyed the chance to complain about their past math experiences, blame their old teachers or old school for their current predicament, and basically take a break for the day from actually doing math. It's not a bad thing to stop a disastrous lesson and have A Talk.

posted by subdee at 1:14 PM on June 2, 2014

In the article she talks about how she "lost it" and had a "meltdown." Those are her words. I think that it's important to put the "broken" comments into that context. According to her, and I have no reason to believe that she isn't a reliable narrator, the "what broke you?" discussion was not said with calm restraint. In my experience, having your teacher meltdown when the class doesn't preform to expectations is not a nice break from doing math. She says at the end of her post that "in the end our meltdown and redo took more time than anticipated by me but it was time well worth it," so I guess you could argue that such behaviour is justified, but I personally wouldn't make that argument.

I teach at the university level, so I really haven't been in a situation were I've had a meltdown over children. Therefore my opinion my not be worth much, but her response is still not something that I can support.

posted by Shouraku at 1:32 PM on June 2, 2014 [1 favorite]

I teach at the university level, so I really haven't been in a situation were I've had a meltdown over children. Therefore my opinion my not be worth much, but her response is still not something that I can support.

posted by Shouraku at 1:32 PM on June 2, 2014 [1 favorite]

I have spent way too much time thinking about why this lesson went off the rails. And again, it all comes down to the teacher. She understands the Common Core concept being taught. But she does not understand how she is supposed to teach it.

If you look at the worksheet, there are two types of items you are supposed to put on a number line between 0 and 1. Some of them are decimal numbers, fractions, and visual representations of fractions (like 3/4 of a circle). These have definitively correct answers. A good teacher would tell kids to work on the answers they know how to get correct, before they work on the more nebulous quantities.

The second type of item is more difficult, and answers may vary. The whole point of this lesson is to take an uncertain idea like "it will snow this week" or "you will go to the beach sometime" and associate it with a numeric probability. This is where the critical thinking happens.

It is absolutely proper for the students to seek out correctness, on their way to completing the items. I looked at the photos of the completed assignments, it appears that most kids worked on the numbers first, working on the answers that can definitively be judged correct. Then they worked out from there, to the more uncertain answers like "the Braves will win the World Series."

But of all the answers, there is one in that photo that makes me very happy. The student assigned .75 probability to "If you drop a rock in water, it will sink."

posted by charlie don't surf at 3:47 PM on June 2, 2014 [3 favorites]

If you look at the worksheet, there are two types of items you are supposed to put on a number line between 0 and 1. Some of them are decimal numbers, fractions, and visual representations of fractions (like 3/4 of a circle). These have definitively correct answers. A good teacher would tell kids to work on the answers they know how to get correct, before they work on the more nebulous quantities.

The second type of item is more difficult, and answers may vary. The whole point of this lesson is to take an uncertain idea like "it will snow this week" or "you will go to the beach sometime" and associate it with a numeric probability. This is where the critical thinking happens.

It is absolutely proper for the students to seek out correctness, on their way to completing the items. I looked at the photos of the completed assignments, it appears that most kids worked on the numbers first, working on the answers that can definitively be judged correct. Then they worked out from there, to the more uncertain answers like "the Braves will win the World Series."

But of all the answers, there is one in that photo that makes me very happy. The student assigned .75 probability to "If you drop a rock in water, it will sink."

posted by charlie don't surf at 3:47 PM on June 2, 2014 [3 favorites]

So the kids are broken -- but the "breakage" is so minimal that a 10 minute teacher melt-down is enough to fix them.

Sounds less like "the kids are broken" and more like "I didn't really explain well that this assignment differed from most other assignments".

posted by Bugbread at 7:49 PM on June 2, 2014 [3 favorites]

Sounds less like "the kids are broken" and more like "I didn't really explain well that this assignment differed from most other assignments".

posted by Bugbread at 7:49 PM on June 2, 2014 [3 favorites]

*52 times? Teachers should keep in mind the possibility that pupils are winding them up.*

It was the fifty-third time, proving that it's always some joker that gets you.

posted by BrotherCaine at 5:53 PM on June 6, 2014 [2 favorites]

jjmoney:

Doing lots of worksheets makes a person shitty at math. My teachers in high school had this silly idea of how math works. I was great at the worksheets, and shitty at math. I would say: "what does a derivative mean? What is it for?" They would say: "that's not important. Do the worksheet. Use the variables you're given, fill in the blanks, and do the worksheet." I didn't understand a damned thing about mathematics until I got to college, where luckily I had actual discussion classes about actual mathematics, and we worked through Newton's

Producing students who can blindly manage derivatives and quadratic equations and such is idiotic. Computers can do that. It's neat to be able to do it quickly, but that's really a parlor trick at this point; it's like taking a literature class and testing kids in how fast they read each chapter.

Computers cannot understand the work they're doing. Teach kids to understand, and they'll be able to do the work anyway, and what's more they'll know when to use it. Worksheets are the absolute worst way to teach kids an understanding of what they're doing.

I get the feeling you don't understand what educational rigor is. Rigor in education is not teaching regurgitation. It is not teaching kids to recite dates of Civil War battles, as important as knowing that is. Rigor in education is inculcating understanding, a rigorous understanding, an understanding that can see details as part of a whole.

You're substituting impressive-seeming performance tests for the actual education rigor if understanding. Rigor is not memorizing things.

posted by koeselitz at 10:33 PM on June 6, 2014 [4 favorites]

*"But in lower grades kids need to discuss their feelings in math less, and do more god**** worksheets. Less talking, less discussions, more algebra worksheets. More tests. More intense homework and studying. Let's get these kids great at math, and show them that there are correct answers, and that they can get them."*Doing lots of worksheets makes a person shitty at math. My teachers in high school had this silly idea of how math works. I was great at the worksheets, and shitty at math. I would say: "what does a derivative mean? What is it for?" They would say: "that's not important. Do the worksheet. Use the variables you're given, fill in the blanks, and do the worksheet." I didn't understand a damned thing about mathematics until I got to college, where luckily I had actual discussion classes about actual mathematics, and we worked through Newton's

*Principia Mathematica*together, pausing and discussing it whenever any of us had questions. That is how education works.Producing students who can blindly manage derivatives and quadratic equations and such is idiotic. Computers can do that. It's neat to be able to do it quickly, but that's really a parlor trick at this point; it's like taking a literature class and testing kids in how fast they read each chapter.

Computers cannot understand the work they're doing. Teach kids to understand, and they'll be able to do the work anyway, and what's more they'll know when to use it. Worksheets are the absolute worst way to teach kids an understanding of what they're doing.

*"Let's not get together in a circle and discuss how probability makes us feel. That will only damage the kids who actually want to go on to do something rigorous, and does no favors to those who don't."*I get the feeling you don't understand what educational rigor is. Rigor in education is not teaching regurgitation. It is not teaching kids to recite dates of Civil War battles, as important as knowing that is. Rigor in education is inculcating understanding, a rigorous understanding, an understanding that can see details as part of a whole.

You're substituting impressive-seeming performance tests for the actual education rigor if understanding. Rigor is not memorizing things.

posted by koeselitz at 10:33 PM on June 6, 2014 [4 favorites]

The great thing about truly understanding math on a deep level is that when you forget a concept you can often still remember enough about how it originated to rediscover it from the other basics you know. Learning by rote alone will usually not get you that.

posted by BrotherCaine at 12:11 AM on June 7, 2014 [2 favorites]

posted by BrotherCaine at 12:11 AM on June 7, 2014 [2 favorites]

koeselitz: "

Your anecdote doesn't sound like "doing lots of worksheets makes a person shitty at math" as much as "doing worksheets alone isn't sufficient to make a person good at math".

posted by Bugbread at 3:49 PM on June 7, 2014

*Doing lots of worksheets makes a person shitty at math.*"Your anecdote doesn't sound like "doing lots of worksheets makes a person shitty at math" as much as "doing worksheets alone isn't sufficient to make a person good at math".

posted by Bugbread at 3:49 PM on June 7, 2014

Yeah. Well, I mean: in an ancillary sense, like maybe "wasting the time doing lots of worksheets means that a person has no time or ability to actually learn anything about math, thus making them shitty at math." Or "doing lots of worksheets is often seen as actually learning math, whereas it's really not, so by being forced to do that you end up never knowing about math."

I really do believe this: a whole generation of kids knows and cares very little about math. In truth, the vast majority of people can and should learn about math, and would probably really enjoy it up to a point. But they don't, because they are not taught it correctly. They're taught it by people who think the way to learning is doing worksheets. And when they make mistakes on those worksheets, or don't understand things on those worksheets, they don't have it explained to them, and they don't get a chance to work it out for themselves; they're just basically told "oh, you're not one of the ones that's

So, in effect, this attitude about worksheets has made a whole lot of people in the world shitty at math, and it would have done the same for me if I hadn't been very lucky.

posted by koeselitz at 11:15 PM on June 8, 2014 [1 favorite]

I really do believe this: a whole generation of kids knows and cares very little about math. In truth, the vast majority of people can and should learn about math, and would probably really enjoy it up to a point. But they don't, because they are not taught it correctly. They're taught it by people who think the way to learning is doing worksheets. And when they make mistakes on those worksheets, or don't understand things on those worksheets, they don't have it explained to them, and they don't get a chance to work it out for themselves; they're just basically told "oh, you're not one of the ones that's

*good at math*; that's okay, there aren't many of us anyway" and they move along.So, in effect, this attitude about worksheets has made a whole lot of people in the world shitty at math, and it would have done the same for me if I hadn't been very lucky.

posted by koeselitz at 11:15 PM on June 8, 2014 [1 favorite]

I've observed the effect of this on my brother. Not only did he end up not caring about math, he got frustrated to the point of inadvertently perpetuating the cycle. He just wanted to get his homework done and over with.

posted by aroweofshale at 12:19 AM on June 9, 2014

posted by aroweofshale at 12:19 AM on June 9, 2014

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